(4x%2B3)%3D112-solve-for-x.jpeg "(2x-7)(4x+3)=112 Solve For X")
Solving the Equation (2x-7)(4x+3) = 112
This problem involves solving a quadratic equation. Here's how to do it:
1. Expand the Equation:
First, we need to expand the left side of the equation by using the FOIL method (First, Outer, Inner, Last).
- First: 2x * 4x = 8x²
- Outer: 2x * 3 = 6x
- Inner: -7 * 4x = -28x
- Last: -7 * 3 = -21
This gives us: 8x² + 6x - 28x - 21 = 112
2. Simplify the Equation:
Combine the like terms: 8x² - 22x - 21 = 112
Move the constant term to the left side: 8x² - 22x - 133 = 0
3. Solve the Quadratic Equation:
We can solve this quadratic equation using the quadratic formula:
x = [-b ± √(b² - 4ac)] / 2a
Where a = 8, b = -22, and c = -133
4. Substitute the Values and Calculate:
x = [22 ± √((-22)² - 4 * 8 * -133)] / (2 * 8) x = [22 ± √(484 + 4256)] / 16 x = [22 ± √(4740)] / 16 x = [22 ± 2√1185] / 16
5. Simplify the Solution:
We get two possible solutions:
- x = (22 + 2√1185) / 16
- x = (22 - 2√1185) / 16
These can be simplified further by factoring out a 2 from the numerator, but it's not strictly necessary.
Therefore, the solutions to the equation (2x-7)(4x+3) = 112 are:
- x = (11 + √1185) / 8
- x = (11 - √1185) / 8